Quantitative relations between nearest-neighbor persistence and slow heterogeneous dynamics in supercooled liquids

Using molecular dynamics simulations of a binary Lennard-Jones model of glass-forming liquids, we examine how the decay of the normalized neighbor-persistence function $C_{\rm B}(t)$, which decays from unity at short times to zero at long times as particles lose the neighbors that were present in their original first coordination shell, compares with those of other, more conventionally utilized relaxation metrics. In the strongly-non-Arrhenius temperature regime below the onset temperature $T_{\rm A}$, we find that $C_{\rm B}(t)$ can be described using the same stretched-exponential functional form that is often utilized to fit the self-intermediate scattering function $S(q, t)$ of glass-forming liquids in this regime. The ratio of the bond lifetime $\tau_{\rm bond}$ associated with the terminal decay of $C_{\rm B}(t)$ to the $\alpha$-relaxation time $\tau_\alpha$ varies appreciably and non-monotonically with $T$, peaking at $\tau_{\rm bond}/\tau_\alpha \simeq 45$ at $T \simeq T_{\rm x}$, where $T_{\rm x}$ is a crossover temperature separating the high- and low-temperature regimes of glass-formation. In contrast, $\tau_{\rm bond}$ remains on the order of the overlap time $\tau_{\rm ov}$ (the time interval over which a typical particle moves by half its diameter), and the peak time $\tau_\chi$ for the susceptibility $\chi_{\rm B}(t)$ associated with the spatial heterogeneity of $C_{\rm B}(t)$ remains on the order of $\tau_{\rm imm}$ (the characteristic lifetime of immobile-particle clusters), even as each of these quantities varies by roughly $5$ orders of magnitude over our studied range of $T$. Thus, we show that $C_{\rm B}(t)$ and $\chi_{\rm B}(t)$ provide semi-quantitative spatially-averaged measures of the slow heterogeneous dynamics associated with the persistence of immobile-particle clusters.